Cho \(F\left( x \right) = \frac{1}{{2{x^2}}}\) là một nguyên hàm của \(\frac{{f\left( x \right)}}{x}\).

A. \(\int {f'\left( x \right)\ln x{\rm{d}}x =  - \left( {\frac{{\ln x}}{{{x^2}}} + \frac{1}{{2{x^2}}}} \right)}  + C\)

B. \(\int {f'\left( x \right)\ln x{\rm{d}}x = \frac{{\ln x}}{{{x^2}}} + \frac{1}{{{x^2}}}}  + C\)

C. \(\int {f'\left( x \right)\ln x{\rm{d}}x =  - \left( {\frac{{\ln x}}{{{x^2}}} + \frac{1}{{{x^2}}}} \right)}  + C\)

D. \(\int {f'\left( x \right)\ln x{\rm{d}}x = \frac{{\ln x}}{{{x^2}}} + \frac{1}{{2{x^2}}}}  + C\)